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Question

The radii of internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respctively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder.

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Solution

We have,

The internal base radius of the spherical shell, r1=3 cm,

The external base radius of the spherical shell, r2=5 cm and

The base radius of solid cylinder, r=142=7 cm

Let the height of the cylinder be h.

As,Volume of solid cylinder = Volume of spherical shell

πr2h=43πr3243πr31πr2h=43π(r32r31)r2h=43(r32r31)49×h=43(12527)h=43×9849h=83

So, the height of the cylinder is 83


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